How to plot field lines in sage

I want to plot the field lines of an electric field, take for example that of an electric dipole. How can I do this in sage?

Edit: Perhaps my question was formulated too much in physicist slang... Mathematically I just want to plot the integral curves of a vector field for example: let $\vec{r}(x,y) = (x,y)$, $\vec{E_1} = \frac{\vec{r}}{|r|^{3}}$ and $\vec{E_2}(x,y) = \vec{E_1}(x-1,y)$

Then I want to plot the field lines of $\vec{E} = \vec{E_1} - \vec{E_2}$

5 answers

I'm not sure whether you already have equations to use or not. How you plot these all depends, of course, on how the equations are given. But, here is something. Using information in section D.73.3 of this webpage on quantum mechanics, we need to plot ${(x^2+z^2)}^{(3/2)}=c x^2$ for various values of $c$. The following code produces a plot.